Dades generals |
Nom de l'assignatura: Tècniques Matemàtiques i Estadístiques
Codi de l'assignatura: 568423
Curs acadèmic: 2019-2020
Coordinació: Francesc Xavier Luri Carrascoso
Departament: Departament de Física Quàntica i Astrofísica
crèdits: 6
Programa únic: S
Hores estimades de dedicació |
Hores totals 150 |
Activitats presencials |
60 |
- Teoria |
60 |
Treball tutelat/dirigit |
40 |
Aprenentatge autònom |
50 |
Recomanacions |
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Competències que es desenvolupen |
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Objectius d'aprenentatge |
Referits a coneixements
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Blocs temàtics |
1. Fundamental of Probability Theory and Statistics
* * General review of probability theory: Random variables and events. Bayes theorem. Probability distributions: binomial, Poisson, Gaussian, Cauchy. Law of large numbers. Hoeffding’s inequality. Central-limit theorem and Berry-Eseen theorem.
* Introduction to R.
* Statistical inference: Point Estimation Theory, Confidence Intervals, Chi-2 tests, Fisher Information, Cramer-Rao bound, Maximum-likelihood estimators, hypothesis testing, Kolmogorov-Smirnov Tests, Least Squares, Information Theory (Typicality, mutual information, correlations).
2. Monte Carlo Methods
* * Generalities. Sampling, Integration, Optimisation.
* Importance sampling, stratified sampling, rejection sampling.
* Metropolis algorithm. Generalities: reversibility, strong ergodicity and convergence. A priori probabilities, parallel tempering, simulated annealing.
* Applications of the Metropolis algorithm to statistical Physics, quantum field theory and events generation.
3. Multivariate analysis and statistical treatment techniques
* * Data analysis and representation. Statistical distances. Principal component analysis.
* Hierarchical and non-hierarchical clustering.
* Discriminant analysis.
* Neural networks.
* Support vector machines.
* Non-parametric methods of estimation of a probability density function: histograms, simple estimators, kernel estimators.
4. Databases and data mining
* * Basic concepts
* Introduction to data mining
* Case study: the Gaia archive.
5. Practical Work
* * Introduction to R
* Introduction to WEKA (data analysis and data mining)
Avaluació acreditativa dels aprenentatges |
There will be no exam for this course. Instead, 5 problem assignments will be given during the course. Grading will be based on the evaluation of the reports provided.
Avaluació única - |
Fonts d'informació bàsica |
Consulteu la disponibilitat a CERCABIB
Llibre
Crawley, Michael J. The R book. Chichester : Wiley & Sons, 2007
DeGroot, Morris H. Probability and statistics. 4th ed. Boston : Pearson Education, cop. 2012
https://cercabib.ub.edu/iii/encore/record/C__Rb1536375?lang=cat
https://cercabib.ub.edu/iii/encore/record/C__Rb1727639?lang=cat
Article
Weinzierl, Stephan. "Introduction to Monte Carlo method", a: http://arxiv.org/abs/hep-ph/0006269
Són conferències |